[1]} propose to learn \(\theta \)  using weakly supervised learning on query-answer pairs without ground-truth parses.
This is challenging because the supervision signals (rewards) are delayed and sparse. For example, whether the generated parse is correct or not is only known after a complete parse is generated and the KB lookup answer is returned.
The authors use an approximate reward, which is dense, for training.
A partial parse is converted to a query to search the KB, and the overlap of its answer with the gold answer is used as the training supervision. A higher overlap indicates a better partial parse.
